It’s normal for birds to call to each other, even if they have never been caged together. In fact, the reason birds learn to talk is in an effort to communicate with us. The problem with opening the cage when she screams is that you are teaching her to scream to get what she wants. If you don’t work on this now, you will get to the point that you can’t stand hearing her all the time. Parrots do not understand punishment – they learn by positive reinforcement, the reward system. When she is quiet, even for just one minute, go to her and praise her and give her a treat. When she screams for attention or to get out, ignore her. Do not give her any type of attention until she is quiet, and then after being quiet for a minute, go to her an reward her. If she screams, walk away without doing anything. She wants a reaction, and she needs to learn that being quiet gets her a reaction, not being loud. You must be consistent – if you give in once, you undo the progress you have made and basically you are starting over. So work with her this way and soon she will learn not to scream to get what she wants.
Letting them play together is fine as long as there is no mating going on.
Thanks for the update,